Preheat oven to 350°F. Place squash cut side down in a glass dish. Cook in microwave for 20 minutes on HIGH, until almost tender. In a saucepan over medium heat, melt butter and add celery and onion; sauté until transparent. Stir in mushrooms; cook 2 to 3 minutes more. Sprinkle with salt, pepper, and parsley. Divide mixture in half, spoon into the squash and cover. Cook 15 minutes in the preheated 350°F oven. Uncover, sprinkle with cheese, and put back in the oven until cheese bubbles.